Steering a 3D limit-cycle walker for collaboration with a leader

Input-to-State Stability of Periodic Orbits of Systems With Impulse Effects via Poincaré Analysis

“…This approach has been successful in generating asymptotically stable periodic gaits for bipedal robots through a variety of methods, including hybrid zero dynamics [6], [7], geometric control [8], virtual holonomic constraints [9], to name a few. Recent extensions of these methods resulted in generating continuums of limit-cycle S. Veer gaits for bipedal walkers [10], [11], and switching among them [12]- [14], to enlarge the behavioral repertoire of these robots in order to accomplish tasks that require adaptability to typical human-centric environments [15], and human (or robot) collaborators [16]. Practical use of these robots demands robustness to external disturbances, which has led many researchers-including the authors of the present paper-to analyze [17]- [19] and design [14], [20], [21] controllers that enhance the robustness of limit-cycle walking gaits.…”

Safe Adaptive Switching among Dynamical Movement Primitives: Application to 3D Limit-Cycle Walkers

“…where p E is the point at which the force is applied and K L and N L are suitable stiffness and damping matrices, respectively; see [1], [2], [29] for more details.…”

“…More details on the model can be found in [37] with the difference due to the existence of the external force, which is taken into account as explained in [2].…”

“…Each controller results in a limit cycle O p that corresponds to a straight-line or a turning walking motion. The controllers are designed within the HZD framework as in [2], [37], and they guarantee exponential stability of O p in the absence of the external force. In the interest of space, we will only discuss some important properties of the controllers Γ p ; details can be found in [2].…”

“…The controllers are designed within the HZD framework as in [2], [37], and they guarantee exponential stability of O p in the absence of the external force. In the interest of space, we will only discuss some important properties of the controllers Γ p ; details can be found in [2]. Associated to each Γ p is a zero dynamics surface Z p which, for each p ∈ P, has the following properties:…”